Finite Group Databasebeta

← #16832200

Subgroups — #16832200

Order 3712.

396 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271872C211yesmaximal, characteristic, complemented
2#14271834C211yesmaximal, characteristic, complemented
3#14271528C211yesmaximal, characteristic, complemented
4#14271526C211yesmaximal, characteristic, complemented
5#14271508C211yesmaximal, characteristic, complemented
6#14271463C211yesmaximal, characteristic, complemented
7#14271462C211yesmaximal, characteristic, complemented
8#14271452C211yesmaximal, characteristic, complemented
9#14271358C211yesmaximal, characteristic, complemented
10#14271356C211yesmaximal, characteristic, complemented
11#14271356C211yesmaximal, characteristic, complemented
12#14271291C211yesmaximal, characteristic, complemented
13#14271272C211yesmaximal, characteristic, complemented
14#14271243C211yesmaximal, characteristic, complemented
15C29×#442C211yesmaximal, characteristic, complemented
16C2×#90805—21no—
17C2×D8×C29C2211yescharacteristic
18C4×D4×C29C2211yescharacteristic
19C4×D4×C29C2211yescharacteristic
20#11745302C2211yescharacteristic
21#11745302C2211yescharacteristic
22D4×Dic29C2211yescharacteristic
23D4×Dic29C2211yescharacteristic
24C2×#90782C2211yescharacteristic
25C2×#90782C2211yescharacteristic
26#11745292—21no—
27#11745286—21no—
28C2×#90779—21no—
29#11745255C2211yescharacteristic
30#11745255C2211yescharacteristic
31#11745252C2211yescharacteristic
32#11745250C2211yescharacteristic
33#11745246—21no—
34#11745246—21no—
35#11745240—21no—
36#11745240—21no—
37#11745236C2211yescharacteristic
38#11745232C2211yescharacteristic
39C4×Dic58C2211yescharacteristic
40C29×#106C2211yescharacteristic
41C29×#102C2211yescharacteristic
42C29×#102C2211yescharacteristic
43C29×#97C2211yescharacteristic
44#11745180C2211yescharacteristic
45#11745180C2211yescharacteristic
46#11745169C2211yescharacteristic
47#11745169C2211yescharacteristic
48#11745169C2211yescharacteristic
49#11745169C2211yescharacteristic
50#11745163C2211yescharacteristic
51#11745162C2211yescharacteristic
52#11745162C2211yescharacteristic
53C8×Dic29C2211yescharacteristic
54#11745157C2211yescharacteristic
55#11745157C2211yescharacteristic
56#11745156C2211yescharacteristic
57#11745155C2211yescharacteristic
58C4⋊#6597C2211yescharacteristic
59C2×D4×C29C2311yescharacteristic
60C2×D4×C29C2311yescharacteristic
61C22×C4×C29—21no—
62C22×C4×C29—21no—
63C2×C22⋊D29—21no—
64C2×C22⋊D29—21no—
65C2×C22⋊D29—21no—
66C2×C22⋊D29—21no—
67C22×Dic29—21no—
68C22×Dic29—21no—
69#90805—44no—
70C2×D116—21no—
71C2×D116—21no—
72C2×D116C2311yescharacteristic
73C2×D116C2311yescharacteristic
74C2×C4×D29—21no—
75C2×C4×D29—21no—
76C2×Dic58—21no—
77C2×Dic58D411yescharacteristic
78D8×C29—22no—
79C2×C8×C29C2311yescharacteristic
80C2×C8×C29C2311yescharacteristic
81C4⋊C4×C29C2311yescharacteristic
82C4⋊C4×C29C2311yescharacteristic
83C22⋊C4×C29—21no—
84C22⋊C4×C29—21no—
85C42×C29C2311yescharacteristic
86C22⋊Dic29—21no—
87C22⋊Dic29—21no—
88#90782—22no—
89#90782—22no—
90#90781—21no—
91#90781—21no—
92C4⋊Dic29—21no—
93C4⋊Dic29D411yescharacteristic
94C4⋊Dic29C2311yescharacteristic
95C4⋊Dic29C2311yescharacteristic
96#90779—21no—
97#90779—21no—
98#90779—21no—
99#90779—21no—
100#90779D411yescharacteristic
101#90779D411yescharacteristic
102C4×Dic29C2311yescharacteristic
103C4×Dic29C2311yescharacteristic
104C2×#6597C2311yescharacteristic
105C2×#6597C2311yescharacteristic
106C23×C29—21no—
107C23×C29—21no—
108C22×D29—21no—
109C22×D29—21no—
110D4×C29—21no—
111D4×C29—21no—
112D4×C29—21no—
113D4×C29#4112yescomplemented
114C2×C4×C29—21no—
115C2×C4×C29—21no—
116C2×C4×C29—42no—
117C2×C4×C29—81no—
118C2×C4×C29C2×D411yescharacteristic
119C2×C4×C29C2×D411yescharacteristic
120C2×C4×C29C2411yescharacteristic
121C22⋊D29—42no—
122C22⋊D29—42no—
123C22⋊D29—81no—
124C22⋊D29—81no—
125C2×Dic29—21no—
126C2×Dic29—21no—
127C2×Dic29—42no—
128C2×Dic29—81no—
129C2×Dic29C2×D411yescharacteristic
130C2×Dic29C2×D411yescharacteristic
131C2×Dic29C2×D411yescharacteristic
132C2×Dic29C2×D411yescharacteristic
133D116—21no—
134D116—21no—
135D116—21no—
136D116—21no—
137D116—42no—
138D116—81no—
139C4×D29—42no—
140C4×D29—42no—
141Dic58—22no—
142Dic58—81no—
143C8×C29—21no—
144C8×C29—21no—
145#6597—21no—
146#6597—21no—
147#3366—291nomaximal, Sylow
148C22×C29—22no—
149C22×C29—41no—
150C22×C29—41no—
151C22×C29—41no—
152C22×C29—41no—
153C22×C29—41no—
154C22×C29C22×D411yescharacteristic
155C2×D29—41no—
156C2×D29—41no—
157C2×D29—41no—
158C2×D29—41no—
159C2×D29—41no—
160C2×D29—41no—
161C4×C29—21no—
162C4×C29—21no—
163C4×C29—41no—
164C4×C29—41no—
165C4×C29C2×#4111yescharacteristic
166C4×C292−1+411yescharacteristic
167Dic29—21no—
168Dic29—21no—
169Dic29—21no—
170Dic29—41no—
171Dic29—41no—
172Dic29AGL(1,ℤ/8)12yes—
173#554—291no—
174#550—291no—
175#490—291no—
176#490—291no—
177#486—291no—
178#478—291no—
179#478—291no—
180#476—291no—
181#459—291no—
182#459—291no—
183#459—291no—
184#446—291no—
185#442—291no—
186#442D2911yescharacteristic, complemented
187C4×D8—291no—
188C2×C29—42no—
189C2×C29—81no—
190C2×C29#54811yescharacteristic
191C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
192C2×C29#57611yescharacteristic
193D29—81no—
194D29—81no—
195C2×#41—581no—
196C2×D8—291no—
197C2×D8—291no—
198C2×D8C2×D2911yescharacteristic
199C4⋊Q8—291no—
200#127—291no—
201#127—291no—
202#127—291no—
203#125—291no—
204#125—291no—
205C22⋊Q8—581no—
206C22⋊Q8—581no—
207C22⋊Q8—581no—
208#121—581no—
209#121—581no—
210#121—581no—
211C4×Q8—291no—
212C4×D4—291no—
213C4×D4—291no—
214C4×D4—291no—
215C4×D4—291no—
216C4×D4C2×D2911yescharacteristic
217C4×D4C2×D2911yescharacteristic
218C2×C4⋊C4—581no—
219#107—291no—
220#106—291no—
221#106C2×D2911yescharacteristic
222C4⋊C8—291no—
223C4⋊C8—291no—
224C4⋊C8—291no—
225#102—291no—
226#102—291no—
227#102—291no—
228#102—291no—
229#102—291no—
230#102—291no—
231#102—291no—
232#102—291no—
233#102C2×D2911yescharacteristic
234#102C2×D2911yescharacteristic
235#97—291no—
236#97C2×D2911yescharacteristic
237C4×C8—291no—
238C29#336611yescharacteristic, complemented, Sylow
239#41—1164no—
240C2×Q8—291no—
241C2×Q8—581no—
242C2×D4—291no—
243C2×D4—291no—
244C2×D4—581no—
245C2×D4—581no—
246C2×D4—581no—
247C2×D4—581no—
248C2×D4—581no—
249C2×D4—581no—
250C2×D4C22×D2911yescharacteristic
251C2×D4C22×D2911yescharacteristic
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—581no—
255C22×C4—581no—
256C22×C4—581no—
257C22×C4—581no—
258D8—22no—
259D8—582no—
260D8—582no—
261C2×C8—291no—
262C2×C8—291no—
263C2×C8C22×D2911yescharacteristic
264C2×C8C22×D2911yescharacteristic
265C4⋊C4—291no—
266C4⋊C4—291no—
267C4⋊C4—291no—
268C4⋊C4—291no—
269C4⋊C4—291no—
270C4⋊C4—581no—
271C4⋊C4—581no—
272C4⋊C4—581no—
273C4⋊C4—581no—
274C4⋊C4—581no—
275C4⋊C4C22×D2911yescharacteristic
276C4⋊C4C22×D2911yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—581no—
280C22⋊C4—581no—
281C22⋊C4—581no—
282C22⋊C4—581no—
283C42—291no—
284C42—291no—
285C42C22×D2911yescharacteristic
286C23—21no—
287C23—21no—
288C23—581no—
289C23—581no—
290Q8—582no—
291Q8—2321no—
292D4—21no—
293D4—21no—
294D4—21no—
295D4—581no—
296D4—581no—
297D4—581no—
298D4—581no—
299D4—1162no—
300D4—1162no—
301D4—1162no—
302D4—2321no—
303D4—2321no—
304D4—2321no—
305D4#9080512yescomplemented
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—42no—
309C2×C4—81no—
310C2×C4—291no—
311C2×C4—291no—
312C2×C4—291no—
313C2×C4—291no—
314C2×C4—581no—
315C2×C4—581no—
316C2×C4—1162no—
317C2×C4—1162no—
318C2×C4—1162no—
319C2×C4—2321no—
320C2×C4D4×D2911yescharacteristic
321C2×C4D4×D2911yescharacteristic
322C2×C4C23×D2911yescharacteristic
323C8—21no—
324C8—21no—
325C8—581no—
326C8—581no—
327C22—22no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—1161no—
334C22—1161no—
335C22—1161no—
336C22—1161no—
337C22—1161no—
338C22—1161no—
339C22C2×D4×D2911yescharacteristic
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—292no—
345C4—581no—
346C4—581no—
347C4—581no—
348C4—1161no—
349C4—1161no—
350C4C2×#9080511yescharacteristic
351C4#1174536511yescharacteristic
352C2—42no—
353C2—81no—
354C2—2321no—
355C2—2321no—
356C2#1427182211yescharacteristic
357C2AGL(1,ℤ/8)×D2911yescharacteristic
358C2#1427196711yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#442C2
socleC22×C29C22×D4
hypercenter#442D29
hypocenterC29#3366
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #14271872C2semidirect
2. #14271834C2semidirect
3. #14271528C2semidirect
4. #14271526C2semidirect
5. #14271508C2semidirect
6. #14271463C2semidirect
7. #14271462C2semidirect
8. #14271452C2semidirect
9. #14271358C2semidirect
10. #14271356C2semidirect
11. #14271356C2semidirect
12. #14271291C2semidirect
13. #14271272C2semidirect
14. #14271243C2semidirect
15. C29×#442C2semidirect
113. D4×C29#41semidirect
186. #442D29semidirect
238. C29#3366semidirect
305. D4#90805semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#142718722
#142718342
#142715282
#142715262
#142715082
#142714632
#142714622
#142714522
#142713582
#142713562
#142712912
#142712722
#142712432
C29×#4422
#336629